Internal problem ID [11803]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+8 y^{\prime }+16 y=8 \,{\mathrm e}^{-2 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve([diff(y(x),x$2)+8*diff(y(x),x)+16*y(x)=8*exp(-2*x),y(0) = 2, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = 4 \,{\mathrm e}^{-4 x} x +2 \,{\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 21
DSolve[{y''[x]+8*y'[x]+16*y[x]==8*Exp[-2*x],{y[0]==2,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 e^{-4 x} \left (2 x+e^{2 x}\right ) \]